Deviation inequallities for exponential jump-diffusion processes

B. Laquerrière^a, N. Privault<sup>b

a</sup> Laboratoire de Mathématiques, Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex, France
^b Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong

Abstract: We clarify the connection between diffusion processes and partial differential equations of the parabolic type. The emphasis is on degenerate parabolic equations. These equations are a generalization of the classical Kolmogorov equation of diffusion with inertia which may be treated as the Fokker-Planck-Kolmogorov equations for the respectively degenerate diffusion processes. The basic results relating to the fundamental solution and the correct solvability of the Cauchy problem are presented.

Keywords: Deviation inequalities, exponential jump-diffusion processes, concentration inequalities, forward/backward stochastic calculus.

MSC: Primary 60F99; Secondary 39B62, 60H05, 60H10

Language: English

Bibliographic databases:

• 
•